A friend who admitted that he saw a lot of sense in Imamiyyah beliefs, said he has difficulty believing in error-free Imams, because everyone in this world is a sinner. How should I answer such a person?

As a general rule everyone is a sinner. It would be helpful to explain that this does not apply to the Holy Prophet (PBUH) or the Imams from his progeny (PBUH) because:
1. They were thoroughly purified.

2. Allah wanted His message delivered in order to remind humanity to refrain from sinning. This could not be achieved via people who were not pure and free of error themselves.

3. It is recorded in the hadith of The Two Precious and Significant Matters – Thaqalain – that the Twelve Imams are both inseparable from, and equal to, the Holy Qur’an. This means that, in the same way as the Qur'an has been safeguarded from falsehood, so too have the Prophet (PBUH) and his progeny (A.S).
I give below some references for Thaqalain from Sunni books:
Sahih Muslim – Section on the Merits of the Companions, Tradition 4425.
Sunan al-Daremi – Section on The Merits of The Qur’an, Tradition 3182.
Musnad Ahmad ibn Hanbal, Traditions, 10681, 10707, 10779.
Mustradak al-Hakim al-Nishaburi Vol. 3, p. 148.
al-Khasis al-Nissa’i, p. 35, Beirut ed.
Hilyat al-Awliya’, Vol. 1, p. 355, Cairo ed.

Ibn Hajar, in his book al-Sawa’iq al-Muhriqah, p. 148, records the above ahadith on the authority of 25 companions.

Sayyid Hashim Bahrani, in his book Ghayat al-Maram, mentions 39 chains of Sunni narrators and 82 chains of Shi’ah narrators regarding hadith – thaqalain.